Journal of Risk

In this issue of The Journal of Risk, derivative pricing in incomplete markets, capital allocation in an enterprise risk management context, and a new coherent risk measure are presented from a theoretical perspective, with a view toward applications. In addition, two empirical studies on standard approaches to the delta hedging of options and volatility time scaling are included.

We begin with "Acceptability bounds for forward starting options using disciplined convex programming", in which Dilip B. Madan and King Wang show how to determine bid and ask prices for an illustrative derivative. Their approach relies on applying a fast convex optimization technique for high dimensions to the dual of the hedging problem associated with the derivative. The authors demonstrate that the resulting bid and ask prices are substantially tighter than they would have been had alternative methods been used.

In the second paper, "Compositional methods applied to capital allocation problems", Jaume Belles-Sampera, Montserrat Guillen and Miguel Santolino prove that capital allocation can be analyzed from the perspective of compositional methods, which emphasize relative information over absolute values. In this approach, capital allocation is driven by rankings. The authors illustrate this method using an insurance case. They show that it accounts for the riskiness of an agent relative to others in the same firm, contrasting it with allocations based on individual agent diversification.

"Delta-hedged gains and risk-neutral moments" by Dahea Kim and Sol Kim is the third paper in this issue. The authors conduct an empirical study of the performance of delta-hedging strategies for options that account for higher-order moments of risk-neutral distributions. Based on recent data that spans a wide spectrum of moneyness and maturities, they show that delta-hedged gains are negatively correlated with ex ante skewness and kurtosis for call options, but positively correlated for put options.

In the issue's fourth paper, "Scaling by the square-root-of-time rule: an empirical investigation using five market indexes", James Cameron, Chandra Gulati and Yan-Xia Lin assess the robustness of the common scaling rule for value-at-risk(VaR) estimation based on daily data across a variety of markets. The sampling period of eleven years considered in this study covers a range of economic cycles, including the global financial crisis of 2007-9. For the standard five- and ten-day windows, the authors contrast constant and generalized autoregressive conditional heteroscedasticity (GARCH) volatility models. Their results favor five-day scaling with the exponential GARCH specification.

Our fifth and final paper is "Shortfall deviation risk: an alternative for risk measurement" by Marcelo Brutti Righi and Paulo Sergio Ceretta. This sees the authors propose a coherent risk measure, shortfall deviation risk (SDR), which combines the expected shortfall risk measure with a dispersion measure, accounting for losses in excess of the shortfall. Through real and simulated data, the authors suggest that SDR can be more robust and more accurate than the common risk measures of expected shortfall and VaR.

Farid AitSahlia
University of Florida